Alonso Mudarra (c. 1508 - 1580) was a Spanish composer for vihuela and renaissance guitar.  Mudarra was also a priest (canon of the cathedral of Seville).  In 1546, Mudarra's book, Tres libros de musica en cifras para vihuela  was published in Seville.  Tres Libros is primarily a vihuela book, but it also contains the earliest surviving music for the renaissance guitar.  The vihuela and guitar music in Tres Libros is written in Italian Tablature.  Mudarra indicates tunings for the renaissance guitar in his book, at the top of each page.  Temple Nuevos ("new tuning") uses the same set of tuning intervals as the 1st 4 strings of the modern guitar.  Temple Viejos ("old tuning") is identical to the new tuning, except the 4th course (equivalent to the 4th string of the modern guitar) is tuned one whole step lower (that is, to play the "old tuning," a modern guitar would require the 4th string to be tuned to "C" rather than "D").  All but one of Mudarra's guitar pieces use the "new tuning" and can therefore be played on the modern instrument with no retuning required (the first guitar Fantasia in Tres Libros is the only piece that requires the "old tuning").

Cover page of Mudarra's Tres Libros (1546).

Click on the player above to hear Mudarra's Fantasia X (demo recording from yours truly).  This is Mudarra's most famous composition.  I'm rather fond of it myself.

Facsimile of the first two pages of Mudarra's Fantasia X (the pieces takes up 5 pages in all).  The tuning intervals required for Mudarra's vihuela music is the same as the lute.  To play this piece on the modern guitar, the 3rd string should be tuned to F#, or otherwise, the F# needs to be played on the 4th string of the guitar.